Ficino doesn't explicitly mention the tetractys, but Farndell's note, like Romano Alberti in 1604, assumes it, so it must be clear to anyone steeped in this literature that this is what Ficino is talking about. 16th century editions often have marginal notes by the editors making such allusions explicit, so I would bet that Piscina's edition of Ficino, whether Latin or a translation, would have mentioned the Pythagorean tetractys.

Here is a 1557 Latin edition of Ficino's commentary on Timaeus, for those who would compare (printed by Antoine Vincent (1500?-1568), Lyon). This is an edition Piscina could have conceivably used. Our note to this passage - p. 33, note 18 - refers to a 1576 edition. This was lazy on our part, since 1576 is too late for Piscina to have used it.

I regret that we didn't give much thought to Piscina's Latin and Greek sources, since he uses so few compared to Anonymous. With Anonymous, it became clear that, despite his erudtion, he relied on Italian translations rather than Latin or Greek editions. I have not yet found an Italian translation of Ficino's commentary on Timaeus from before 1565. Possibly Hankins mentions this somewhere - volume 2 of Plato in the Italian Renaissance appears to have an exhaustive bibliography of 16th century editions of Plato. Mike, do you have it?

Interlibrary loan finally delivered the Ficino to me. I went to post the relevant material, and Ross had already done it, including the notes, much more comprehensively than I had planned to do. And thanks for supplying Ficino's Latin original as well as the English translation. I was wondering about that. Piscina surely would have known Latin, no need for Italian, except for the notes that might have come with it, and perhaps mistranslations, especially of "plenitud-" words (however unlikely, since the Italian is so similar). Which is to say, yes, it would be good to track down any translations of the Ficino before 1565.

So in referring to these chapters of Ficino, Piscina, and anyone else familiar with Ficino's commentary, would have known that he was using a Pythagorean tradition. The very idea of describing "the properties of the number four" as note 18 to Ross et al's edition of Piscina puts it (p. 33 at https://books.google.com/books?id=RnxeD ... se&f=false), is a Pythagorean project. Ficino uses the word "Pythagoreans" explicitly, in both chapter 20 and 24.

For reference in what comes later in this post here is Ficino's chapter 20:

Chapter 20 The first consideration: why the number four in relation to the elements befits the world

BUT MORE OF these things elsewhere. Let us now go back to the division of the cosmos into parts, so that we may be able to descry their harmonious composition. We were saying earlier that the numbers five and six han-nonise with the spherical shape of the world. Now we are saying that the number four, too, matches its fullness. Indeed, four first fulfils all the difference of the numbers, embracing within itself the first even number and the first odd number. Four also fulfils the simple sequence of numbers, since with its limits it fulfils ten, perfectly completing ten with one, two, three, and four. Again, it fills the development of dimensions, achieving this with four limits: point, length, breadth, and depth. It fulfils musical harmony, for between its limits are held the double, the triple, the quadruple, the sesquialteral, the sesquitertial, the diapason, the disdiapason, the diapente, and the diatessaron. It fulfils nature, which extends as far as four limits by means of substance, quantity, quality, and movement. In short, it fulfils all, whether it be something within nature or something above nature, through essence, being, power, and action.

The followers of Pythagoras were therefore justified in using the number four to designate the fullness of the cosmic body and the cosmic soul and to testify on oath that the fount of ever-flowing nature is fourfold. It is undoubtedly from this fount that the four elements emanate. Hence the fourfold triplicity in the heavens. Hence the four seasons under the heavens. Hence, beneath time, there appear the four humours, the four complexions, and the four dispositions. Hence, above time, there arise the four virtues. Hence, in eternity, there are the four models of the virtues.

No "perfect number" is mentioned here. but they were not only part of Pythagoreanism but of the standard trivium as well; Euclid had a formula for some of them (see Wikipedia). But in Ficino ch. 20 the word is "plenitudini" and "plenitudinem", which Farndell translates as "fullness". Piscina in talking about the "quaternary number" (numero quadernario, Caldwell et al p. 26) as "more perfect" {piu perfetto) than others has mixed up "plenitudino" with "perfectus", an easy thing to do, since "perfectus" means "finished, completed, perfect, excellent, exquisite" (per Wiktionary), and if something partakes of fullness, it is completed as well. The difference is that while four is a number characterizing plenitude, it is not a perfect number. This is a fairly minor difference when you consider what the "fullness" of four was used for: to justify the completeness of the list of four "model virtues", of four and only four gospels (by Irenaeus), of three spatial dimensions (as a solid is specified by a minimum of four points), four seasons, four humors, and so on.

However Piscina does more than say that four is perfect, probably intending to mean the number of completion. He says it is more perfect than any other number. That can only refer to the tetraktys, the quaternity that contains all. (Thanks very much, Ross and Alain, for presenting the scholarship on that "-ktys" and especially that Alberti in 1604, Ross). So the fourness is not the number four, but a special quaternity, the quaternity of numbers contained in the quaternary number, i.e. the set of all the numbers up to four, which in being ten contains all the numbers. It is not the most perfect number - perfection does not admit of more or less, and if any is, it would be 6 - but it is the most revered, given that the Pythagoreans "testify on oath that the fount of ever-flowing nature is fourfold", as Ficino tells us. That which the Pythagoreans swore by was the tetraktys.

We may then wonder how there could be a fifth suit, if four is a complete set. The beginning of Chapter 21 suggests one answer, namely, that if the four comprise the cosmos, the fifth would be from beyond the cosmos, the supersensible realities upon which the cosmos is based. This fits their role in the game, too, as triumphing over all the others. It in turn divides into four. Ficino says:

Again, if I did not fear prolixity on the one hand and novelty on the other, I would list some remarkable statements by Iamblichus, Syranus, and Proclus, who designate four levels higher than the celestial world: One, Limit, Limitlessness, Combination.

It strikes me that Alain's division of the 22 into 1+4+7+10 could correspond to these four Neoplatonic divisions. The 1 is the One, of which the Bateleur is an image, the 4 are the archetypes of those who set limits; the 7 is the boundlessness of human feeling, action, and thought; and the 10 is the tetraktys itself, all the numbers through combination, and specifically the 4 of Death through Fire (earth, water, air, and fire, reflecting the archetypal four levels), the 3 of the celestials, the 2 of the end of time, and the 1 of the Divine Fool.

Of the group of 4 from Death to Fire Piscina only has two: the Demoni, in the air, as one mean, and Fire as the second mean, between things earthly and things celestial. Of the first he says (Caldwell et al, p. 23):

...it has been the opinion of many, in particular the Platonists, that the Demoni are spirits that are in the air & that they are somehow in the middle between gods and men.

And of the second (Ibid):

After the Demoni comes Fire, as the due mean between the stars, which are celestial, and mundane things...

However Plato's two means in the Timaeus (31b-32c), and Ficino's in his commentary, Ch. 23, were between earth and fire; here Death would naturally represent earth and Temperance, with the water between two jugs, as water. In another Neoplatonic way of seeing Temperance, it would be the lower part of the air, which Ficino has as the level just above earth in chapter 21. The lower air is the region inhabited by the soul immediately after death, with what Plotinus and Ficino after him called the "airy body" (Ficino, Commentary on the Phaedrus, trans. Allen, p. 75, snippets at https://books.google.com/books?id=qIc-4 ... dy&f=false). The soul in that body can enter our dreams and appear as ghosts. Below it was the "earthy body" (Ibid.) and above it the "fiery body" and others (Plotinus Enneads, 4.3.9: "a soul leaving an aerial or fiery body for one of earth", at http://www.sacred-texts.com/cla/plotenn/enn295.htm; for others, 4.3.15).

I cannot attribute the overall analysis of the tarot sequence I have presented to Piscina, of course. However it is not far from his thinking, and I see no reason why it could not have been one way of seeing the tarot in Neopythagorean/Neoplatonic terms over the next couple of centuries.

Note added next day: I added a few more page references, as well as online inks to Piscina and to Ficino and Plotinus on the "airy body".

Back for a little time.
Thanks Ross for offering the Ficino's translations.

Bravo Mikeh!
What a beautiful analys of the fifth suit in a neo pythagorean manner.
It's the best commentary I ve ever seen on the topic.
We may then wonder how there could be a fifth suit, if four is a complete set. The beginning of Chapter 21 suggests one answer, namely, that if the four comprise the cosmos, the fifth would be from beyond the cosmos, the supersensible realities upon which the cosmos is based. This fits their role in the game, too, as triumphing over all the others. It in turn divides into four. Ficino says:

Again, if I did not fear prolixity on the one hand and novelty on the other, I would list some remarkable statements by Iamblichus, Syranus, and Proclus, who designate four levels higher than the celestial world: One, Limit, Limitlessness, Combination.

It strikes me that Alain's division of the 22 into 1+4+7+10 could correspond to these four Neoplatonic divisions. The 1 is the One, of which the Bateleur is an image, the 4 are the archetypes of those who set limits; the 7 is the boundlessness of human feeling, action, and thought; and the 10 is the tetraktys itself, all the numbers through combination, and specifically the 4 of Death through Fire (earth, water, air, and fire, reflecting the archetypal four levels), the 3 of the celestials, the 2 of the end of time, and the 1 of the Divine Fool.

Of the group of 4 from Death to Fire Piscina only has two: the Demoni, in the air, as one mean, and Fire as the second mean, between things earthly and things celestial. Of the first he says (Caldwell et al, p. 23):

...it has been the opinion of many, in particular the Platonists, that the Demoni are spirits that are in the air & that they are somehow in the middle between gods and men.

And of the second (Ibid):

After the Demoni comes Fire, as the due mean between the stars, which are celestial, and mundane things...

However Plato's two means in the Timaeus (31b-32c), and Ficino's in his commentary, Ch. 23, were between earth and fire; here Death would naturally represent earth and Temperance, with the water between two jugs, as water. In another Neoplatonic way of seeing Temperance, it would be the lower part of the air, which Ficino has as the level just above earth in chapter 21. The lower air is the region inhabited by the soul immediately after death, with what Plotinus and Ficino after him called the "airy body" (Ficino, Commentary on the Phaedrus, trans. Allen, p. 75, snippets at https://books.google.com/books?id=qIc-4 ... dy&f=false). The soul in that body can enter our dreams and appear as ghosts. Below it was the "earthy body" (Ibid.) and above it the "fiery body" and others (Plotinus Enneads, 4.3.9: "a soul leaving an aerial or fiery body for one of earth", at http://www.sacred-texts.com/cla/plotenn/enn295.htm; for others, 4.3.15).

I cannot attribute the overall analysis of the tarot sequence I have presented to Piscina, of course. However it is not far from his thinking, and I see no reason why it could not have been one way of seeing the tarot in Neopythagorean/Neoplatonic terms over the next couple of centuries.

Circa 21 + 1 years ago was first published the initial presentation to the public of the arithmological structure of the standard tarot.
Looking back until now, I want to thank all the contributors to this topic - whatever the point of view.
Special thanks to the main contradictors :
Jess Karlin, James Rewak, Michael Hurst, Huck Meyer
Special thanks to those who remained politely silent :
Thierry Depaulis, Ross Caldwell
Special thanks to those who were "neutral" with an open interested mind :
Stuart Kaplan, Bob O' Neill, Robert Place, JM David, Steve Mangan
Special thanks to the very few whose support never failed
Andrea Vitali, Michael Howard